The subject matter of the present invention relates to a new Pulsed Nuclear Magnetic Resonance (NMR) well logging apparatus using a multi-wait time pulsed nuclear magnetic resonance (NMR) logging method for processing a plurality of multi-wait time spin echo pulse sequences which are output from a pulsed nuclear magnetic resonance (NMR) tool when the tool is traversing a wellbore.
Commercial and experimental pulsed NMR logging methods and apparatus, which acquire depth logs from a continuously moving logging sonde, have employed the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. The CPMG pulse sequence is defined in eq. (1) of the this specification and in U.S Pat. No. 5,291,137 issued to Freedman (hereafter called "the Freedman patent"). Recalling eq. 1 of the Freedman patent and part A of this specification, the CPMG pulse sequence for a phase alternated pair can be written in the form: EQU CPMG.sup.(.+-.) :W-90.degree.(.+-.x)-(t.sub.cp -180.degree.(y)-t.sub.cp -(echo).sub.j).sub.j=1,2, . . . ,J. ( 1)
For purposes of the present discussion, the important ingredient in {:he above equation describing the CPMG pulse sequences is the wait time (W) that precedes each set of radio frequency (RF) pulses that produce the spin echoes. A detailed description of the action of the RF pulses is given in part A of this specification. Here we note that a watt time is required so that the nuclear magnetization which produces the spin-echo signals can approach its thermal equilibrium value (in the magnetic field produced by a permanent magnet in the tool sonde). During depth logging with a continuously moving logging tool, the pulse sequence in eq. 1 is repeated, as the tool traverses the borehole, using a single wait time (W) which is approximately 1.0 second in duration. In many reservoir rock formations, the magnetization attains only a fraction of its thermal equilibrium value (e.g., its maximum attainable value at a given temperature) during the wait time and therefore the logs of the NMR properties must be corrected to account for the fact that the wait time is too short. Increasing the wait time is not a viable solution because it is inefficient and leads to reduced logging speeds which is undesirable for a commercial well logging service.
The single wait time CPMG pulse sequence described above produces spin-echo waveforms that, by signal processing, are used to compute T.sub.2 -distributions of the the porous rock formations traversed by the NMR tool. The T.sub.2 -distributions are used to compute the NMR logs. Because only a single wait time (W) is utilized, the spin echo waveforms have no direct sensitivity to the T.sub.1 -distributions which determine the rate at which the magnetization approaches its thermal equilibrium value during the wait time (W). Thus an accurate correction for insufficient wait time is not possible using a single wait time pulsed NMR logging method. The Freedman patent introduced a parameter called the T.sub.1 /T.sub.2 ratio (denoted in the Freedman patent by the Greek symbol .xi.) which was utilized in the signal processing algorithm as a means for correcting the log outputs for insufficient wait time. The correction is based on an empirical relationship established by Kleinberg, et al. (see references 11 and 12 in part B of this specification) which relates the T.sub.1 and T.sub.2 -distributions of porous rock samples. The Kleinberg, et al. work in references 11 and 12 showed that at the low frequencies (e.g., in the 2 MHz range) at which pulsed NMR logging tools operate, the two relaxation time distributions are approximately congruent (i.e., have the same shape and size). Moreover it was shown that T.sub.1 .tbd..xi.T.sub.2. The Kleinberg, et al. publication in reference 11 shows that the true value of the ratio .epsilon. varies from one rock sample to the next. The correction for finite wait time used in the Freedman patent assumed a constant (and incorrect) value for .epsilon. since the true value is not known and can not be determined using the single wait time CPMG pulse sequence disclosed in the teachings of the Freedman patent.
It is useful to review the Freedman patent since the invention disclosed here utilizes the teachings of the Freedman patent and also discloses improved new apparatus and methods for eliminating the inherent accuracy problem associated with the teachings of the Freedman patent.
In the U.S. Pat. No. 5,291,137 issued to Freedman, a nuclear magnetic resonance (NMR) tool known as the Combinable Magnetic Resonance Tool (CMR tool), also formerly known as the Pulsed Nuclear Magnetism Tool (PNMT), is disposed in a wellbore (hereinafter, the CMR tool will be known as the "NMR tool"). The NMR tool produces a nuclear magnetization in a formation traversed by the wellbore by applying a static magnetic field B.sub.0 to the formation. The magnetic field is produced by a permanent magnet located in the logging tool. The nuclear magnetization is produced during a predetermined wait time W which is followed by a set of radio frequency (rf) pulses which produce the measured spin-echo signals from the rock formations. Following the rf pulses the nuclear magnetization is practically zero and another wait time is required to re-establish the magnetization prior to application of the next set of rf pulses. During the wait time, the magnetic moments of the protons contained in the fluids (gas, oil and water) align themselves along the direction of the static magnetic field B.sub.0. Ideally, the wait time W would be chosen to be sufficiently long so that the magnetic moments are completely aligned with the field B.sub.0 as shown schematically in FIG. 5 of the Freedman patent. In practice, this can require wait times as long as 10 seconds in some reservoirs but these wait times would be impractical for a moving logging tool. It is undesirable to increase the wait time because for a desired vertical resolution of the NMR measurement the logging speeds would be decreased in proportion and would be too slow for a commercial logging service. In practice wait times are selected to be generally less than 3 seconds for continuous logging so that a correction for insufficient wait time (or equivalently, for incomplete recovery of the total nuclear magnetization following the set of rf pulses) must be applied in many situations.
After the wait time W, the logging tool begins energizing the formation with a plurality of rf pulses starting with the Bx90 pulse and continuing with the By180 pulses as shown in FIG. 9a of the Freedman patent. Then, the NMR tool begins to receive a plurality of spin echo pulses from the formation as shown in FIG. 9b of the Freedman patent. A predetermined total number (say J) of spin-echoes are collected by application of J By180 pulses. After collection of the J spin-echoes the total nuclear magnetization is practically zero and a wait time W initiates the next CPMG and so forth as the tool traverses the borehole. Note that the wait times used to initiate each CPMG are identical (i.e., equal to W). The rf pulses and spin-echoes of a CPMG waveform are shown schematically in FIGS. 9a and 9b of the Freedman patent, respectively.
In order to compensate for the insufficient wait time, the processing method and apparatus disclosed in the Freedman patent utilizes a correction parameter .xi. (hereinafter, the parameter .xi. used in the Freedman patent will be denoted by .xi..sub.0) which is an approximation to the true T.sub.1 /T.sub.2 ratio of the rock formations being logged.
However, an additional problem exists: the parameter .xi..sub.0 approximating the true T.sub.1 /T.sub.2 ratio is always assumed to be a constant value. Even if the .xi..sub.0 parameter were allowed to vary with the measurement depth, there still exists no method for accurately determining the proper value from measurements made in a borehole using a single wait time pulse sequence. The use of approximate ratios (.xi..sub.0) which differ from the true ratios (.xi.) can lead to inaccurate results. In real terms, true T.sub.1 /T.sub.2 ratio varies from one rock sample to another. An experimental study by Kleinberg, et. al. (see ref. 11 in part B of this specification) found for a wide range of rock types that the ratios varied approximately from 1.0 to 2.6. The ratios differ depending upon the particular rock material of the particular formation being excited. Therefore, it is incorrect to use a constant value, .xi..sub.0, for the ratio.
Since the function used to correct for insufficient wait time (see eq. (5) of the Freedman patent) which compensates for the insufficient wait time (W) utilizes a constant and/or assumed value of the ratio parameter, the resultant T.sub.2 -distributions or equivalently, the set of spectral amplitudes ({.alpha..sub.l }) in the Freedman patent can be inaccurate.
Recall that the N.sub.s spectral amplitudes, denoted collectively by the set {.alpha..sub.l }, are computed by constructing and minimizing the negative logarithm of a maximum likelihood function shown in eq. (42) and in block 4A3 of FIG. 13 of the Freedman patent. Recall also that the negative logarithm of the likelihood function (-ln L) in eq. (42) is a function of the aforementioned assumed ratio (.xi..sub.0).
In the Freedman patent, the set of spectral amplitudes {.alpha..sub.l } were used to generate the output record medium shown in FIG. 16 of the Freedman patent. Therefore, since the spectral amplitudes are inaccurate, the output record medium shown in FIG. 16 of the Freedman patent is also somewhat inaccurate.
Through the use of computer simulations, this specification demonstrates that pulsed NMR logging methods utilizing single wait time pulse seqences include an uncontrolled approximation which can lead to significant accurracy errors in the output logs. This problem represents a deficiency in all other methods for obtaining depth logs that use single wait time pulse sequences. The root of the problem can be traced to the arbitrary variability of the true T.sub.1 /T.sub.2 ratios (i.e., the variability of T.sub.1) in rocks and specifically to the use of a constant and/or assumed ratio, say .epsilon..sub.0, to process the logs which is not equal to the true value, .xi.. To avoid confusion with notation it is worth pointing out that the constant ratio in the Freedman patent was denoted by .xi. instead of .xi..sub.0 which is used in the present invention to differentiate between the assumed value and the true value.
In accordance with the present invention, part B of this specification discloses a new apparatus for acquiring multi-wait time CPMG pulse sequences and a method for processing the resulting spin-echo waveforms which eliminates the accuracy problems inherently associated with single wait time pulse sequences, the new apparatus functioning to generate a multi-wait time pulse sequence which can be succinctly defined using eq. (72) of part B of this specification. That is, the multi-wait time pulse sequence is described by the following notation: EQU CPMG.sup.(.+-.) :{n.sub.p {W.sub.p -90.degree.(.+-.x)-(t.sub.cp -180.degree.(y)-t.sub.cp -(echo).sub.j).sub.j=1,2, . . . ,J.sbsb.p }}.sub.p=1,2, . . . ,N.sbsb.wt) ( 72)
which consists, in its general form, of n.sub.p phase alternated pair (PAP) CPMG waveforms, each initiated with a wait time W.sub.p where p=1, 2, . . . N.sub.wt. The integers n.sub.p specify the number of repeats of PAP waveforms with wait time W.sub.p in a multi-wait time pulse sequence. For short wait times the repeat PAP waveforms can be averaged to improve the S/N ratio of the measurement. The integer N.sub.wt specifies the number of different wait times in the multi-wait time pulse sequence and J.sub.p is the total number of echoes collected for wait time W.sub.p. Note that if N.sub.wt =1, the above multi-wait time pulse sequence is equivalent to the single wait time pulse sequence of the Freedman patent. A multi-wait time pulse sequence is defined here to correspond to N.sub.wt &gt;1. Part B of this specification discloses a method for using the plurality of PAP waveforms corresponding to the different wait times, W.sub.p, using the teachings of the Freedman patent to compute sets of estimated apparent spectral amplitudes denoted by, {.alpha..sub.l,p }, for each wait time. These apparent spectral amplitudes are in many situations inaccurate when the wait times, W.sub.p, are too short for the magnetization to achieve complete recovery and because the estimates are made using an assumed and inaccurate value of the T.sub.1 /T.sub.2 ratio (.xi..sub.0). For a multi-wait time pulse sequence, the apparent spectral amplitudes, {.alpha..sub.l,p }, and assumed ratio, .xi..sub.0, are input as parameters into a cost function derived in part B of this specification. The cost function is set forth in eq. (73) of this specification. The cost function also depends on variables representing the true (i.e., intrinsic) spectral amplitudes, ({.alpha..sub.l }), and the true T.sub.1 /T.sub.2 ratio (.xi.) of the rock formation producing the measured spin-echo signals. Simultaneous minimization of the cost function with respect the aforementioned variables provides estimates of the true T.sub.1 /T.sub.2 ratios (the estimates are denoted by .xi.) and an updated T.sub.2 -distribution denoted by the spectral amplitudes, {.alpha..sub.l }. The updated spectral amplitude estimates are used to compute updated log outputs. This process is shown schematically in the flowchart of FIG. 36.
The most relevant prior art related to the present disclosure is U.S. Pat. No. 5,023,551 issued to Kleinberg et al. entitled "Nuclear Magnetic Resonance Pulse Sequences for Use With Borchole Logging Tools." Kleinberg, et al. disclose a multi-wait time pulse sequence which combines fast inversion recovery and CPMG spin-echo sequences (referred to in the patent as the "FIR/CPMG" pulse sequence) for the purpose of making non-linear estimations of longitudinal relaxation times (T.sub.1), transverse relaxation times (T.sub.2), and total signal amplitudes (or equivalently formation porosities) from various models including stretched exponential and multi-exponential models. The continuous logs of the aforementioned quantities obtained from the FIR/CPMG pulse sequence were later shown by Kleinberg, et al., in a paper presented at the 1993 Society of Petroleum Engineers Annual Meeting (see reference 11 of part B of this specification), to be non-repeatable at bed boundary interfaces. The repeatability problem can be traced to the long measurement times required by the FIR/CPMG pulse sequence and the poor signal to noise of the non-linear estimations required by the teachings of the Kleinberg, et al. patent. The aforementioned work of Kleinberg, et al. and also similar works which utilized FIR/CPMG pulse sequences for laboratory studies, and which are cited in reference 6 of part A and reference 12 of part B of this specification, proved to be impractical for borehole logging tools. The Kleinberg, et al. U.S. Pat. No. 5,023,551 discloses in claim 42 a "saturation recovery/CPMG" pulse sequence in which the inversion pulses are omitted from the FIR/CPMG pulse. However, although the Kleinberg claim 42 pulse sequence appears to be identical to the pulse sequence in eq. (72) discused above, Kleinberg's claim 42 pulse sequence does not disclose the integers n.sub.p which represents the explicit repeats of CPMG pulse sequences with different wait times, W.sub.p. Futhermore, the saturation recovery/CPMG pulse sequence was not disclosed by Kleinberg, et al. in connection with any means for generating a more accurate output record medium by computing more accurate estimates of true T.sub.2 -distribution (e.g., spectral amplitudes), {.alpha..sub.l } and estimates of true T.sub.1 /T.sub.2 ratios (.xi.).